integral from-4 to 0 of 2x^3+12x^2+16x

解

\int_{- 4}^{0} 2 x^{3} + 12 x^{2} + 16 x d x

0

解答ステップ

\int_{- 4}^{0} 2 x^{3} + 12 x^{2} + 16 x d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 4}^{0} 2 x^{3} d x + \int_{- 4}^{0} 12 x^{2} d x + \int_{- 4}^{0} 16 x d x

\int_{- 4}^{0} 2 x^{3} d x = - 128

\int_{- 4}^{0} 12 x^{2} d x = 256

\int_{- 4}^{0} 16 x d x = - 128

= - 128 + 256 - 128

簡素化

= 0